Question: What is the period of $y = \cos \frac{x}{2}$?
Solution: The graph of $y=\cos \frac{x}{2}$ passes through one full period as $\frac{x}{2}$ ranges from $0$ to $2\pi,$ which means $x$ ranges from $0$ to $\boxed{4 \pi}.$

The graph of $y=\cos \frac{x}{2}$ is shown below:

[asy]import TrigMacros;

size(400);

real g(real x)
{
	return cos(x/2);
}

draw(graph(g,-3*pi,3*pi,n=700,join=operator ..),red);
trig_axes(-3*pi,3*pi,-2,2,pi/2,1);
layer();
rm_trig_labels(-5, 5, 2);
[/asy]